Excuse me, I want to burn incense with my girlfriend. I used to be alone, but now I am alone. What rules should I pay attention to?

You can go together, but it is best not to hold hands and kiss or say some sweet words in the Buddhist temple, that is to say, don't do these couples' actions in the temple to show respect for the three treasures.

If you are interested in Buddhism after reading my answer, you can look at the Buddhist materials recommended by me in my personal profile of my last school.